What is the extreme f(x)=3x^{2/5}-x^{3/5} ?

The extreme f(x)=3x^{2/5}-x^{3/5} is Minimum(0,0),Maximum(32,4)

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extreme f(x)=3x^{2/5}-x^{3/5}

extreme points

f (x) = 3 x^{\frac{2}{5}} - x^{\frac{3}{5}}

Minimum (0, 0), Maximum (32, 4)

Solution steps

f^{'} (x) = \frac{6}{5 x ^{\frac{3}{5}}} - \frac{3}{5 x ^{\frac{2}{5}}}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 32,

Decreasing

: 32 < x < \infty

Plug

x = 0

into

3 x^{\frac{2}{5}} - x^{\frac{3}{5}} : 0

Minimum (0, 0)

Plug

x = 32

into

3 x^{\frac{2}{5}} - x^{\frac{3}{5}} : 4

Maximum (32, 4)

Minimum (0, 0), Maximum (32, 4)

\frac{x + 1}{2 x + 1}

f (x) = \frac{6 x}{sin ( x )}

f (x) = \frac{x + 3}{x ^{2} - 4}

f (x) = 4 (x - 3)^{5}

f (x) = 2 x^{2} - 8 x, x \geq 2

What is the extreme f(x)=3x^{2/5}-x^{3/5} ?
The extreme f(x)=3x^{2/5}-x^{3/5} is Minimum(0,0),Maximum(32,4)